have the casing formed in concrete. Plate-steel casings with either end or top inlets are commonly used. For the higher heads, cast iron casings are most popular. Either type of wheel may employ two runners on one shaft.
Characteristic.-—If A = head available, feet, n = revolutions per minute desired P = horsepower oi each turbine at the runner, the specific speed or characteristic is n8 = n\/P - ^- This is that ideal speed (revolutions per minute) which a similar wheel would have if operating under 1 ft. head and then developing 1 hp. Each design has its own specific speed: when size is changed by change of scale (all dimensions changed proportionately) the specific speed does not change.
The best values of ns are from 1 to 4 for tangential and from 30 to 60 for reaction turbines. Allowable values for the former are up to 8 (per nozzle) and for the latter from 10 to 100, but extreme values lead to low efficiencies. If the available head and required power and speed lead to abnormal values of ns, some adjustment is possible by varying the number of units. Thus if 2,550 hp. were required at 750 r.p.m. with 100 ft. head, n, would be 120, a value not permissible. By using two wheels (or runners) of 1,275 hp. each, an allowable value results. In some cases the speed could be changed. ' The equation for specific speed leads to the following forms:
mPi X = nfj* At constant speed, ^ = (r) : Power varies much more rapidly than head.
f 2 \A2/
At constant head, j^ = (— j : power varies inversely as the square of the speed. At constant power, — = (*"/ ' sPee<* vai>ies much more rapidly than head.
.. 60 70 80 90 100 Characteristic Speed,ns
FIG. 31.—Practical limits for turbine runners.
These relations hold for wheels of a given series. They do not include the effect of varying efficiency.
^ The accompanying chart shows the low limits practicable for specific or characteristic speed at various heads. If speeds are made lower, the runner passages become very long and narrow, the diameter great and the cost high.